Illinois Journal of Mathematics

Random walk on the incipient infinite cluster on trees

Martin T. Barlow and Takashi Kumagai

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Abstract

Let $\mathcal{G}$ be the incipient infinite cluster (IIC) for percolation on a homogeneous tree of degree $n_0 + 1$. We obtain estimates for the transition density of the continuous time simple random walk $Y$ on $\mathcal{G}$; the process satisfies anomalous diffusion and has spectral dimension 4/3.

Article information

Source
Illinois J. Math., Volume 50, Number 1-4 (2006), 33-65.

Dates
First available in Project Euclid: 12 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258059469

Digital Object Identifier
doi:10.1215/ijm/1258059469

Mathematical Reviews number (MathSciNet)
MR2247823

Zentralblatt MATH identifier
1110.60090

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Citation

Barlow, Martin T.; Kumagai, Takashi. Random walk on the incipient infinite cluster on trees. Illinois J. Math. 50 (2006), no. 1-4, 33--65. doi:10.1215/ijm/1258059469. https://projecteuclid.org/euclid.ijm/1258059469


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